Iwasawa theoretic invariants for modules arising from the Iwasawa theory of ordinary Galois representations
provide key insights into the arithmetic of such objects. Of particular interest is the behaviour of these invariants when one considers two ordinary Galois representations whose associated residual representations are isomorphic. Greenberg and Vatsal [1]} initiated such a study for elliptic curves, and this was developed further in the works of Emerton-Pollack-Weston [2]}. Similar investigations were carried out in the context of non-commutative Iwasawa theory in, for instance, [3]} and [4]}.
